Updated 4 p.m. | Rep. Jeff Denham wants a vote on his bill that would allow illegal immigrants brought to the country as children to gain permanent residence in the United States in exchange for military service — and he's got a plan in the works.

The California Republican is looking for Democrats and Republicans who are members of the House Armed Services Committee to sign on as co-sponsors of his legislation, known as the ENLIST Act, a House GOP aide familiar with Denham's efforts told CQ Roll Call. "We are working to gather co-sponsors from both sides of the aisle," Denham spokeswoman Jordan Langdon said in a statement.

The panel is set to mark up the fiscal 2015 National Defense Authorization Act in the weeks ahead and Denham, who is not himself a HASC member, needs to shore up support among committee members who would be willing to vote on the ENLIST Act if it were offered as an amendment to the underlying bill.

Denham also needs a lawmaker on the committee to introduce the amendment, which shouldn't be a problem: Of the 42 co-sponsors of the ENLIST Act, 11 of them are HASC members, including the chairman, Howard "Buck" McKeon, R-Calif.

McKeon, however, has not yet committed to supporting efforts to place the amendment into the bill, either in advance of or during the course of the markup, a Republican committee aide told CQ Roll Call on Thursday.

The aide noted that any member of the panel is free to offer an amendment during the full committee markup so long as the language was "solely the jurisdiction" of the Armed Services Committee. Denham's bill has only been referred to one committee, Armed Services, and would only change U.S. military code, not immigration law — which falls under the purview of the Judiciary Committee.

Another Republican HASC co-sponsor is Veterans Affairs Chairman Jeff Miller, R-Fla., who told CQ Roll Call that while the final decision would be up to McKeon, bringing up the amendment in the committee could be a worthwhile endeavor.

"It's worthy of discussion," Miller said. "I feel that if somebody has worn the uniform of this country, the least we could do is to help them and their future."

The remaining co-sponsors on the Republican side of the HASC aisle are Reps. Duncan Hunter of California, Joe Heck of Nevada, Jon Runyan of New Jersey, Austin Scott of Georgia and Brad Wenstrup of Ohio; Democratic committee members and co-signers are Reps. Colleen Hanabusa of Hawaii, Andre Carson of Indiana, Bill Enyart of Illinois and Marc Veasey of Texas.

That leaves 50 HASC members in all to target for their support, and Denham has his work cut out for him.

Ultimately the bill's fate depends on GOP leadership. If the ENLIST Act makes it into the defense authorization bill in committee, it could sink the whole measure on the floor. A conservative faction of the House Republican Conference is unwilling to support any legislative effort to rewrite the nation's immigration laws, particularly those that deal with the legal status issue.

Alternatively, if leaders allow the ENLIST Act to be made in order for consideration as an amendment to the defense authorization on the House floor, they could risk exposing members to a politically toxic vote in an election year. Even co-sponsor Kevin McCarthy, the House's No. 3 Republican, might decide it's not the right time to force the issue.

Denham actually did have his amendment made in order during last year's floor debate, but it was withdrawn before members were forced to vote. This time around, as one of just three House GOP co-sponsors of a comprehensive immigration overhaul bill being touted by House Democrats, he may not be able to promise his leadership that he won't, if given the chance, demand a tally of the "yeas" and "nays," even if it's on a procedural vote should its germaneness be challenged.